ON THE κ-REGULAR SEQUENCES AND THE GENERALIZATION OF F-MODULES

Title & Authors
ON THE κ-REGULAR SEQUENCES AND THE GENERALIZATION OF F-MODULES

Abstract
For a given ideal I of a Noetherian ring R and an arbitrary integer $\small{{\kappa}{\geq}-1}$, we apply the concept of $\small{{\kappa}}$-regular sequences and the notion of $\small{{\kappa}}$-depth to give some results on modules called $\small{{\kappa}}$-Cohen Macaulay modules, which in local case, is exactly the $\small{{\kappa}}$-modules (as a generalization of f-modules). Meanwhile, we give an expression of local cohomology with respect to any $\small{{\kappa}}$-regular sequence in I, in a particular case. We prove that the dimension of homology modules of the Koszul complex with respect to any $\small{{\kappa}}$-regular sequence is at most $\small{{\kappa}}$. Therefore homology modules of the Koszul complex with respect to any filter regular sequence has finite length.
Keywords
$\small{{\kappa}}$-regular M-sequences;$\small{{\kappa}}$-depth;$\small{{\kappa}}$-ht;local cohomology modules;$\small{{\kappa}}$-Cohen Macaulay modules;f-modules;$\small{{\kappa}}$-modules;Koszul complexes;
Language
English
Cited by
References
1.
Kh. Ahmadi-Amoli, Filter regular sequences, local cohomology modules and singular sets, Ph. D. Thesis, University for Teacher Education, Iran, 1996.

2.
Kh. Ahmadi-Amoli and N. Sanaei, The consepts of k-regular sequences and k-height of an ideal, Preprint.

3.
M. Brodmann and L. T. Nhan, A finitness result for associated primes of certain extmodules, Comm. Algebra 36 (2008), no. 4, 1527-1536.

4.
N. Q. Chinh and L. T. Nhan, On the associated primes and the support of local cohomology modules, Algebra Colloq. 15 (2008), no. 4, 599-608.

5.
R. Lu and Z. Tang, The f-depth of an ideal on a module, Proc. Amer. Math. Soc. 130 (2002), no. 7, 1905-1912.

6.
H. Matsumura, Commutative Ring Theory, Cambridge University Press, 1986.

7.
L. Melkersson, Some applications of a criterion for artinianness of a module, J. Pure Appl. Algebra 101 (1995), no. 3, 291-303.

8.
U. Nagal and P. Schenzel, Cohomological annihilators and Castelnuovo-Mumford regularity, Commutative algebra: syzygies, multiplicities, and birational algebra (South Hadley, MA, 1992), 307-328, Contemp. Math., 159, Amer. Math. Soc., Providence, RI, 1994.

9.
L. T. Nhan, On generalized regular sequences and the finiteness for associated primes of local cohomology modules, Comm. Algebra 33 (2005), no. 3, 793-806.

10.
P. Schenzel, N. V. Trung, and N. T. Cuong, Verallgemeinerte Cohen-Macaulay-Moduln, Math. Nachr. 85 (1978), 57-73.

11.
N. Zamani, Cohen-Macaulay modules in dimension > s and results on local cohomology, Comm. Algebra 37 (2009), no. 4, 1297-1307.